1.
Consider two complete vector fields on R^n. Is it known if their Lie
bracket is complete?
2.
On a (finite-dimensional) connected manifold, is it known when the Lie
algebra of all vector fields that commute with a fixed vector field is
finite-dimensional?
More generally, is it known when the Lie algebra of all vector fields
V that preserve a given tensor X, in the sense that the Lie derivative
L_V X = 0, is finite-dimensional?
Re: lie algebra ... why is the lie algebra of a lie group and its identity componet the same. ... As for the Lie bracket, proving that it is same in both cases depends ... space at the identity with the left-invariant vector fields and use this ... this is true for any manifold.... (sci.math)
Re: classification of Lie groups ... >> which is the only one with a corresponding compact Lie group.... >> compact real form of a complex simple Lie algebra.... (sci.math.research)
Re: Lie groups and Lie alegbras -- some simple questions ... > has a pretty good knowlege of working with Lie groups and such. ... There are indeed 3 maps to which the term adjoint is applied. ... Then there is the action of G on the Lie algebra LG by ... gives rise to a Lie algebra homomorphism f:LG->LG. ... (sci.math)
Re: Palais Theorem - Counterexample? ... the lie algebra Xof vector fields is the Lie algebra of ... a vector field giving rise to an action (the flow ... In theoretical physics symmetries often are threated in terms of lie ... (sci.math)
Re: Palais Theorem - Counterexample? ... If G is a simply connected Lie Group, M a compact manifold and phi:... *g* denotes the Lie algebra of G, XXthe Lie algebra of smooth ...vector fields") and Diffthe diffeomorphism group on M, ... (sci.math)
